Due Mar 9, 3:59 AM EDT
Let A and B be two events. What is A∩B?
A coin tossed 3 times. Let A be event First tossing yields head and B be event Exactly one tail occurred. How many outcomes belongs to event A∩B?
Only two outcomes satisfy both events: HTH and HHT. Indeed, the first position should be H because it belongs to A. Only one T should be placed on one of the other positoins, giving exactly two outcomes.
A coin tossed 3 times. Let A be event First tossing yields head and B be event Exactly one tail occurred. How many outcomes belong to event A∪B?
Event A consists of outcomes {HHH, HHT, HTH, HTT}. Event B consists of outcomes {THH, HTH, HHT}. Event A∪B is their union. Only THH is not present in A, so we should add it. The union has 5 elements.
A coin tossed 3 times. Let A be event At least one tossing yields head. How many outcomes belong to event A?
If event At least one tossing yields head did not occur, it means that no tossing yielded head. The only possible outcome is TTT.